Question

An object of mass , m is moving with a constant velocity v. How much work should be done on the object in ordered to bring the object at rest

Answer 1

object moves with constant velocity
hence, no potential energy of body only kinetic energy .
e.g KE =(1/2)mv^2
we also know conservation of energy theorem ,
change in kinetic energy = workdone by external force
now,
kinetic energy final - kinetic energy initial = workdone by external force
but body finally at rest so, KE f = 0
so,
0- 1/2mv^2 = workdone by external force

so, workdone by external force = -1/2mv^2

Answer 2

method 1.....
________

let 'S' be the distance covered before coming into rest.

Body finally comes into rest so it's final velocity = 0 m/s

initial velocity = v

so using v^2 = u^2+ 2aS

find a = {v^2 - u^2} / S = { 0 - v } /S = -v/S

force = mass × acceleration

= m × (-v^2/2S) = -mv/2S

so work done = F×S

= - mv^2/2S × S = -1/2×mv^2 ans...

method 2
_______

from work energy theorem work done by all forces is equal to change in its kinetic energy..

so work done on object = final kinetic energy - initial kinetic energy

so finally body comes to rest so final kinetic energy =0

initial kinetic energy = mv^2/2

work done = 0 - 1/2× mv^2

= - 1/2× mv^2 ans..